I have seen this type of transformer before, but I can never seem to find out what it's actutally called. With this type of transformer it's not the turns ratio that gives the high voltages, it's the capacitance within each bobbin cavity multiplying with the adjacent cavity.

Very strange indeed, and capable of very high voltages!

I've heard it called a capacitance load driver transformer, But I don't think that's the official name for it, as whenever I try to look it up I never find it.

On my monitor, the wire in the bottom coil is a darker orange and appears to be heavier gage. So, it appears at least two coils. That type of segmented winding for the secondary is common in HV transformers.

It is probably a flyback transformer. There is massive insulation on the coils to prevent breakdown. As you stated a flyback transformer doesn't get it's voltage SOLELY from turns ratio. It also produces high voltages by having a large dI/dt. As we all know,

V = L * dI/dt

so, if dI/dt is large, a huge voltage is produced that is proportional to the inductance. It appears that the inductance is set to remain linear by gapping the center tap.

This seem to make sense? This is just guess work on my part...

Oh yeah,

Another indicator that it is probably a flyback is the output diode to rectify the secondary. The normal mode of operation of a flyback is that you charge the inductance of the primary (because the diodes block the secondary from producing forward current), and when the primary is opened, the flyback energy is transfered to the secondary and conducted through the output diodes.

S lannan, the core is sectioned to facilitate assembly. The coils are wound on plastic bobbins and the core is placed afterward. The core only handles magnetic flux, so it is the insulation on the wires and the plastic bobbin that is subjected to voltage.